The following was not sent to this group but may be of general
interest so I am sending it.
To: "Katherine (Williams) Derbyshire" <kewms at kew.com>
Subject: Re: Vector multiplication??
Regarding A^2 where A is a vector.
There is a very powerful element-by-element processing built into
Mathematica that makes it unnecessary to write explicit DO loops for
many things. If A and B are vectors of the same length then
1. A^2 gives the list of the elements squared, A[i]^2;
2. A*B gives the list with elements A[i]*B[i]
3. A + B gives the list with elements A[i]+B[i];
4. A^B is the list with elements A[i]^B[i];
5. A/B is the list with elements A[i]/B[i].
Also if one defines
n=Range[0,10]
then
x^n
is the list
{1,x,x^2,x^3,...,x^10}
All this is very obvious to anyone who knows APL, so its just a
matter of learning the language.